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Download Guide to Essential Math - A Review for Physics, Chemistry by Margaret Dikel, Frances Roehm PDF

By Margaret Dikel, Frances Roehm

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The second egg can then go into any of the remaining 11 cups. So far, there are 12 × 11 132 possible arrangements for these two eggs in the carton. The third egg can go into 10 remaining cups. Continuing the placement of eggs, we will wind up with one of a possible total of 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 distinguishable arrangements. : n! ≡ n(n − 1)(n − 2) · · · 1. 83) The first few factorials are 1! 1, 2! 2, 3! 6, 4! 24, 5! 120. As you can see, the factorial function increases rather steeply.

44) Logarithms Inverse operations are pairs of mathematical manipulations in which one operation undoes the action of the other—for example, addition and subtraction, multiplication and division. The inverse of a number usually means its 1/x. , x−1 rocal) equals 1. Raising to a power and extraction of a root are evidently another pair of inverse operations. An alternative inverse operation to raising to a power is taking the logarithm. 45) in which a is called the base of the logarithm. All the formulas for manipulating logarithms can be obtained from corresponding relations involving raising to powers.

75). 8 Factorials, Permutations, and Combinations Imagine that we have a dozen differently colored eggs that we need to arrange in an egg carton. The first egg can go into any one of the 12 cups. The second egg can then go into any of the remaining 11 cups. So far, there are 12 × 11 132 possible arrangements for these two eggs in the carton. The third egg can go into 10 remaining cups. Continuing the placement of eggs, we will wind up with one of a possible total of 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 distinguishable arrangements.

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